Matrix Algebra with Computational Applications

by Dirk Colbry

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Matrix Algebra with Computational Applications is a collection of Open Educational Resource (OER) materials designed to introduce students to the use of Linear Algebra to solve real world problems. These materials were developed specifically for students and instructors working in a “flipped classroom” model that emphasizes hands-on problem solving activities during class meetings, with students watching lectures and completing readings and assignments outside of the classroom.

Description from LibreTexts.

Publisher
Michigan State University
Subjects
Mathematics, Linear Algebra
Licence
CC BY-NC 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. About the Lead Author
  7. Acknowledgments
  8. 1: Matrix Algebra class preparation checklist
  9. 1.1: Get Jupyter Working
  10. 1.2: Review Python Packages
  11. 1.3: Complete Pre-class Assignment
  12. 2: 01 In-Class Assignment - Welcome to Matrix Algebra with computational applications
  13. 2.0: Introduction
  14. 2.1: Class Procedures
  15. 2.2: Introductions
  16. 2.3: Example
  17. 2.4: Syllabus, Schedule and other Procedures
  18. 2.5: Download and review next pre-class assignment
  19. 3: 02 Pre-Class Assignment - Vectors
  20. 3.0: Introduction
  21. 3.1: Introducing the Course Textbooks
  22. 3.2: Today’s Reading
  23. 3.3: Scalars, Vector and Tensors
  24. 3.4: Assignment wrap-up
  25. 4: 02 In-Class Assignment - Vectors
  26. 4.0: Introduction
  27. 4.1: Example linear system
  28. 4.2: Pre-class assignment review
  29. 4.3: Vectors in Python
  30. 5: 03 Pre-Class Assignment - Linear Equations
  31. 5.0: Introduction
  32. 5.1: System of Linear Equations
  33. 5.2: Visualizing the problem
  34. 5.3: Multidimentional Spaces
  35. 5.4: Matrix Notation
  36. 5.5: Assignment wrap-up
  37. 6: 03 In-Class Assignment - Solving Linear Systems of equations
  38. 6.0: Introduction
  39. 6.1: Pre-class assignment review
  40. 6.2: Jacobi Method for solving Linear Equations
  41. 6.3: Numerical Error
  42. 7: 04 Pre-Class Assignment - Python Linear Algebra Packages
  43. 7.0: Introduction
  44. 7.1: The Syntax for Systems of Linear Equations
  45. 7.2: Introduction to Gauss Jordan Elimination
  46. 7.3: Gauss Jordan Elimination and the Row Echelon Form
  47. 7.4: Gauss Jordan Practice
  48. 7.5: Assignment wrap up
  49. 8: 04 In-Class Assignment - Linear Algebra and Python
  50. 8.0: Introduction
  51. 8.1: Pre Class Review
  52. 8.2: Solving Systems of Linear Equations
  53. 8.3: Underdetermined Systems
  54. 8.4: Practice Curve Fitting Example
  55. 9: 05 Pre-Class Assignment - Gauss-Jordan Elimination
  56. 9.0: Introduction
  57. 9.1: Sympy RREF function
  58. 9.2: Calculating Vector Length, Normalization, Distance and Dot
  59. 9.3: Vector spaces in R^n
  60. 9.4: Assignment wrap up
  61. 10: 05 In-Class Assignment - Gauss-Jordan
  62. 10.0: Introduction
  63. 10.1: Pre-class assignment review
  64. 10.2: Generalize the procedure
  65. 10.3: Basic Gauss Jordan
  66. 11: 06 Pre-Class Assignment - Matrix Mechanics
  67. 11.0: Introduction
  68. 11.1: Dot Product Review
  69. 11.2: Matrix Multiply
  70. 11.3: Identity Matrix
  71. 11.4: Elementary Matrices
  72. 11.5: Solving Many Systems (at the same time)
  73. 11.6: Assignment wrap up
  74. 12: 06 In-Class Assignment - Matrix Multiply
  75. 12.0: Introduction
  76. 12.1: Review of Pre class assignment
  77. 12.2: Systems of Linear Equations with Many Solutions
  78. 12.3: Matrix Multiply
  79. 13: 07 Pre-Class Assignment - Transformation Matrix
  80. 13.0: Introduction
  81. 13.1: The Inverse Matrix (aka A^-1)
  82. 13.2: Transformation Matrix
  83. 13.3: Assignment wrap-up
  84. 14: 07 In-Class Assignment - Transformations
  85. 14.0: Introduction
  86. 14.1: Review of Pre-Class Assignment
  87. 14.2: Affine Transforms
  88. 14.3: Fractals
  89. 15: 08 Pre-Class Assignment - Robotics and Reference Frames
  90. 15.0: Introduction
  91. 15.1: Review
  92. 15.2: 2D Forward Kinematics
  93. 15.3: Assignment wrap-up
  94. 16: 08 In-Class Assignment - The Kinematics of Robotics
  95. 16.0: Introduction
  96. 16.1: Review Pre-class Assignment
  97. 16.2: Pick and Place
  98. 16.3: Odd Clock
  99. 17: 09 Pre-Class Assignment - Determinants
  100. 17.0: Introduction
  101. 17.1: Introduction to Determinants
  102. 17.2: Properties of Determinants
  103. 17.3: One interpretation of determinants
  104. 17.4: Cramer’s Rule
  105. 17.5: Assignment wrap-up
  106. 18: 09 In-Class Assignment - Determinants
  107. 18.0: Introduction
  108. 18.1: Review Pre-class Assignment
  109. 18.2: Algorithm to calculate the determinant
  110. 18.3: Using Cramer’s rule to solve Ax=b
  111. 19: 10 Pre-Class Assignment - Eigenvectors and Eigenvalues
  112. 19.0: Introduction
  113. 19.1: Eigenvectors and Eigenvalues
  114. 19.2: Solving Eigenproblems - A 2x2 Example
  115. 19.3: Introduction to Markov Models
  116. 19.4: Assignment wrap-up
  117. 20: 10 In-Class Assignment - Eigenproblems
  118. 20.0: Introduction
  119. 20.1: Pre Class Review
  120. 20.2: Introduction to Markov Models
  121. 20.3: Another Markov Model Example
  122. 21: 11 Pre-Class Assignment - Vector Spaces
  123. 21.0: Introduction
  124. 21.1: Basis Vectors
  125. 21.2: Vector Spaces
  126. 21.3: Lots of Things Can Be Vector Spaces
  127. 21.4: Assignment wrap-up
  128. 22: 11 In-Class Assignment - Vector Spaces
  129. 22.0: Introduction
  130. 22.1: Review Pre-class Assignment
  131. 22.2: Introduction to subspaces
  132. 22.3: Basis Vectors
  133. 22.4: Vector Spaces
  134. 23: 12 Pre-Class Assignment - Matrix Spaces
  135. 23.0: Introduction
  136. 23.1: Review the Properties of Invertible Matrices
  137. 23.2: The Basis of a Vector Space
  138. 23.3: Change of Basis
  139. 23.4: Assignment wrap-up
  140. 24: 12 In-Class Assignment - Matrix Representation
  141. 24.0: Introduction
  142. 24.1: Review Pre-class assignment
  143. 24.2: Matrix Representation of Vector Spaces
  144. 24.3: Practice Nutrition
  145. 25: 13 Pre-Class Assignment - Projections
  146. 25.0: Introduction
  147. 25.1: Orthogonal and Orthonormal
  148. 25.2: Code Review
  149. 25.3: Gram-Schmidt
  150. 25.4: Assignment wrap-up
  151. 26: 13 In-Class Assignment - Projections
  152. 26.0: Introduction
  153. 26.1: Pre-class Review
  154. 26.2: Understanding Projections With Code
  155. 26.3: Gram-Schmidt Orthogonalization Process
  156. 27: 14 Pre-Class Assignment - Fundamental Spaces
  157. 27.0: Introduction
  158. 27.1: Orthogonal Complement
  159. 27.2: The Four Fundamental Spaces
  160. 27.3: Independent Learning
  161. 27.4: Assignment wrap-up
  162. 28: 14 In-Class Assignment - Fundamental Spaces
  163. 28.0: Introduction
  164. 28.1: Pre-class assignment review
  165. 28.2: Four Fundamental Subspaces
  166. 28.3: Practice Example
  167. 29: 15 Pre-Class Assignment - Diagonalization and Powers
  168. 29.0: Introduction
  169. 29.1: Eigenvalues and eigenvectors review
  170. 29.2: Diagonalizable Matrix
  171. 29.3: Assignment wrap-up
  172. 30: 15 In-Class Assignment - Diagonalization
  173. 30.0: Introduction
  174. 30.1: Pre-class Assignment Review
  175. 30.2: Diagonalization
  176. 30.3: The Power of a Matrix
  177. 31: 16 Pre-Class Assignment - Linear Dynamical Systems
  178. 31.0: Introduction
  179. 31.1: Linear Dynamical Systems
  180. 31.2: Markov Models
  181. 31.3: Ordinary Differential Equations
  182. 31.4: Assignment wrap up
  183. 32: 16 In-Class Assignment - Linear Dynamical Systems
  184. 32.0: Introduction
  185. 32.1: Epidemic Dynamics - Discrete Case
  186. 32.2: Epidemic Dynamics - Continuous Model
  187. 32.3: Population Dynamics
  188. 33: 17 Pre-Class Assignment - Decompositions
  189. 33.0: Introduction
  190. 33.1: Matrix Decomposition
  191. 33.2: Decompositions
  192. 33.3: Assignment wrap-up
  193. 34: 17 In-Class Assignment - Decompositions and Gaussian Elimination
  194. 34.0: Introduction
  195. 34.1: Pre-Class Review
  196. 34.2: Decompositions
  197. 34.3: Focus on LU
  198. 35: 18 Pre-Class Assignment - Inner Product
  199. 35.0: Introduction
  200. 35.1: Inner Products
  201. 35.2: Inner Product on Functions
  202. 35.3: Assignment wrap-up
  203. 36: 18 In-Class Assignment - Inner Products
  204. 36.0: Introduction
  205. 36.1: Pre-class Review
  206. 36.2: Minkowski Geometry
  207. 36.3: Function Approximation
  208. 37: 19 Pre-Class Assignment - Least Squares Fit (Regression)
  209. 37.0: Introduction
  210. 37.1: Least Squares Fit
  211. 37.2: Linear Regression
  212. 37.3: One-to-one and Inverse transform
  213. 37.4: Inverse of a Matrix
  214. 37.5: Assignment wrap-up
  215. 38: 19 In-Class Assignment - Least Squares Fit (LSF)
  216. 38.0: Introduction
  217. 38.1: LSF Pre-class Review
  218. 38.2: Finding the best solution in an overdetermined system
  219. 38.3: Pseudoinverse
  220. 39: 20 In-Class Assignment - Least Squares Fit (LSF)
  221. 39.0: Introduction
  222. 39.1: LSF Example - Tracking the Planets
  223. 39.2: LSF Example - Predator Pray Model
  224. 39.3: LSF Example - Estimating the best Ellipses
  225. 40: Pre-Class Assignment - Solve Linear Systems of Equations
  226. 40.0: Introduction
  227. 40.1: Linear Systems
  228. 40.2: Under Defined Systems
  229. 40.3: Invertible Systems
  230. 40.4: Overdefined systems
  231. 40.5: System Properties
  232. 40.6: Assignment wrap up
  233. 41: 21 In-Class Assignment - Solve Linear Systems of Equations using QR Decomposition
  234. 41.0: Introduction
  235. 41.1: Pre-Class Review
  236. 41.2: Solve Linear Systems
  237. 41.3: Overdetermined Systems
  238. 41.4: Underdetermined Systems
  239. 42: Supplemental Materials - Python Linear Algebra Packages
  240. 42.0: Introduction
  241. 42.1: Matplotlib
  242. 42.2: Review of Python Math Package
  243. 42.3: Review of Python Numpy Package
  244. 42.4: Advanced Python Indexing
  245. 42.5: LaTeX Math
  246. 42.6: Jupyter Tips and Tricks
  247. 43: Jupyter Getting Started Guide
  248. 43.1: Getting Jupyter Working
  249. 43.2: Example running python code in Jupyter Notebooks
  250. 43.3: Video review of Python, IPython, and IPython notebooks
  251. 43.4: Installing Anaconda Python
  252. 43.5: Introduction to the Engineering Jupyter Account
  253. 43.6: More Information
  254. 44: Python Linear Algebra Packages
  255. 44.0: Introduction
  256. 44.1: AnswerCheck tool
  257. 44.2: Review of Python Math Package
  258. 44.3: Review of Python Numpy Package
  259. 44.4: Advanced Python Indexing
  260. 44.5: LaTeX Math
  261. Back Matter
  262. Index
  263. Glossary
  264. Detailed Licensing